This property of operations comes into play when ever you have a string of numbers that are either being multiplied or added. It tells use that the order in which you group or approach the problem does not really matter. For example: 3 + 6 +8 +2 has the same result as if you added the numbers in this form: 6 + 3 +2 + 8. The same applies to multiplication. If we were to multiply 7 with 5 and 4, we could arrange it as 7 x 5 x 4 or 5 x 4 x 7. The final product would be the same regardless of how we arranged it. This solid and detailed section of worksheets will help you to learn how to use the associative property to regroup algebraic expressions, both in adding and in multiplying. This set of worksheets introduces your students to the concept of the associative property, provides examples, short practice sets, longer sets of questions, and quizzes. The associative property helps students transition into early algebra concepts and starts them thinking up that alley. The following worksheets will help your students to understand how to manipulate equations using the associative property.
Print Associative Property Worksheets
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Associative Property Lesson
Learn how to rewrite equations and still have the outcome be the same. This makes for a nice introduction to algebra. Example: (4 + 5) + 3
Worksheet 1
Rewrite these equations to help make them more manageable to work with. This is a skill that will go a long way for you. Example: a + (m + d)
Review Sheet
Practice rewriting the following 6 equations by using what you have learned so far. Example: w(gs)
Skill Quiz
Rewrite these 10 equations that need your love and care to organize. Example: T x (a x h)
Do Now Worksheet
Complete these 3 problems dealing with associative properties and put your answers in the "My Answer" box. This can be done with the whole class as a reminder or quick refresher.
Addition and Multiplication Lesson
This worksheet explains how to rewrite equations using the associative properties of addition and multiplication. A sample problem is solved.
Lesson and Practice
The associative property of addition says that when we add more than two numbers the grouping of the addends does not change the sum. For multiplication it says that when we multiply more than two numbers the grouping of the factors does not change the product.
Rewrite Using Associative Property Worksheet
Students will rewrite equations using the skills that they have learned. Ten problems are provided.
What is the Associative Property?
The associative property, in mathematics, states that the sum or product of three or more numbers will always be the same regardless of their grouping. In mathematics, grouping refers to using parentheses () or brackets []. This property can only be used in addition or multiplication, not subtraction or division.
The formula that use differs based on the operation that you are using:
For Addition: (a + b) + c = a + (b + c)
For Multiplication: (a x b) x c = a x (b x c)
The formula shows the outcome will remain the same regardless of the grouping.
Associative Property of Addition
The sum of three or more numbers also follows the associative property. The sum of these numbers will remain the same no matter how the numbers are arranged. Let’s see some examples so we can better understand the use of this when working with addition:
Example: What if we let a=2, b=5, and c=8. The equation then becomes (2+5) + 8 = 2 + (5+8). Solving the right-hand side will get us 2 + 13 = 15. Solving the left-hand side will get us 7 + 8 = 15. Hence, right hand side = left hand side.
Associative Property of Multiplication
The product of three or more numbers also follows the associative property. The product of these numbers will remain the same no matter how the numbers are arranged. Let’s see some examples to better understand how to use this with multiplication operations:
Example: In the formula for the associative property of multiplication, let a=5, b=3, and c=7. The equation then becomes (5 x 3) x 7 = 5 x (3 x 7). Solving the right-hand side will get us 5 x 21 = 105. Solving the left-hand side will get us 15 x 7 = 105. Hence, right-hand side = left-hand side.
Associative Property of Rational Numbers
The sum or product of three or more rational numbers also follows the associative property. The sum or product of these numbers remains the same no matter how the numbers are arranged. Let’s see some examples to better understand how this works.
Example 1: In the formula of associative property of rational numbers in addition, let a/b=1/2, c/d= 3/4, e/f= 5/6. The equation then becomes (1/2 + 3/4) + 5/6 = 1/2 + (3/4 + 5/6). Solving the right-hand side will get us 1/2 + 19/12 = 25/12. Solving the left-hand side will get us 5/4 + 5/6 = 25/12. Hence, right hand side = left hand side.
Example 2: In the formula of associative property of rational numbers in multiplication, let a/b=1/2, c/d= 3/4, e/f= 5/6. The equation then becomes (1/2 x 3/4) x 5/6 = 1/2 x (3/4 x 5/6). Solving the right-hand side will get us 1/2 x 3/8 = 3/16. Solving the left-hand side will get us 3/8 x 5/6 = 3/16. Hence, right hand side = left hand side.
Note that this does not apply to division or subtraction. As we move into algebra we run into unknown variables, but the operations are the same and this property has the same place. If add or multiply variables, it does not matter how we assemble them. For example, a + b + c = c + a + b. We make heavy use of this property to help us reorganize equations into forms that are easier to work with.
How to Rewrite Equations Using the Associative Property
We use parentheses to group a different pair of numbers together. Meanwhile, we use this property when we are rewriting any number in an expression. Associative Property - With respect to addition: If you are changing the order, the answer will not change. If you have real numbers a, b, c, then, the equation will be like; ( a + b ) + c = a + ( b + c). With respect to multiplication: The result will also be the same while changing the order of the multiplicative numbers. We will suppose the same thing while finding the following expression that is; 5 × 1/3 × 3. Here, we will get the same result by changing the order of the expression. For example; (5 × 1/3) × 3 = (5/3) × 3 = 5 | 5 × ( 1/3 × 3 ) = 5 × 1 = 5. If you have a, b, c as a real number while multiplying the expressions, the equation will be; ( a × b ) × c = a × ( b × c). Rewriting the Equations - With respect to addition: (3+ 0.6) + 0.4. Change the grouping or order -> 3 + ( 0.6 + 0.4 ) = 1. With respect to multiplication: ( - 4 × 2/5 ) × 15 = .Change the order or grouping -> - 4 × ( 2/5 × 15) = 6.